Observation of time quasicrystal and its transition to superfluid time crystal

We report experimental realization of a quantum time quasicrystal, and its transformation to a quantum time crystal. We study Bose-Einstein condensation of magnons, associated with coherent spin precession, created in a flexible trap in superfluid $^3$He-B. Under a periodic drive with an oscillating magnetic field, the coherent spin precession is stabilized at a frequency smaller than that of the drive, demonstrating spontaneous breaking of discrete time translation symmetry. The induced precession frequency is incommensurate with the drive, and hence the obtained state is a time quasicrystal. When the drive is turned off, the self-sustained coherent precession lives a macroscopically-long time, now representing a time crystal with broken symmetry with respect to continuous time translations. Additionally, the magnon condensate manifests spin superfluidity, justifying calling the obtained state a time supersolid or a time super-crystal

Some New/Old Approaches to QCD

This is a talk delivered at the Meeting on Integrable Quantum Field Theories, Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent attempts to revive two old ideas regarding an analytic approach to QCD-the development of a string representation of the theory and the large N limit of QCD.Comment: 20 page

Approximate Homomorphisms of Ternary Semigroups

A mapping $f:(G_1,[ ]_1)\to (G_2,[ ]_2)$ between ternary semigroups will be called a ternary homomorphism if $f([xyz]_1)=[f(x)f(y)f(z)]_2$. In this paper, we prove the generalized Hyers--Ulam--Rassias stability of mappings of commutative semigroups into Banach spaces. In addition, we establish the superstability of ternary homomorphisms into Banach algebras endowed with multiplicative norms.Comment: 10 page

A preliminary factor analytic investigation into the first-order factor structure of the Fifteen Factor Plus (15FQ+) on a sample of Black South African managers

The original publication is available at http://www.sajip.co.zaMoyo, S. & Theron, C. 2011. A preliminary factor analytic investigation into the first-order factor structure of the Fifteen Factor Plus (15FQ+) on a sample of Black South African managers. SA Journal of Industrial Psychology, 37(1), 1-22, doi: 10.4102/sajip.v37i1.934.Orientation: The Fifteen Factor Questionnaire Plus (15FQ+) is a prominent personality questionnaire that organisations frequently use in personnel selection in South Africa. Research purpose: The primary objective of this study was to undertake a factor analytic investigation of the first-order factor structure of the 15FQ+. Motivation for the study: The construct validity of the 15FQ+, as a measure of personality, is necessary even though it is insufficient to justify its use in personnel selection. Research design, approach and method: The researchers evaluated the fit of the measurement model, which the structure and scoring key of the 15FQ+ implies, in a quantitative study that used an ex post facto correlation design through structural equation modelling. They conducted a secondary data analysis. They selected a sample of 241 Black South African managers from a large 15FQ+ database. Main findings: The researchers found good measurement model fit. The measurement model parameter estimates were worrying. The magnitude of the estimated model parameters suggests that the items generally do not reflect the latent personality dimensions the designers intended them to with a great degree of precision. The items are reasonably noisy measures of the latent variables they represent. Practical/managerial implications: Organisations should use the 15FQ+ carefully on Black South African managers until further local research evidence becomes available. Contribution/value-add: The study is a catalyst to trigger the necessary additional research we need to establish convincingly the psychometric credentials of the 15FQ+ as a valuable assessment tool in South Africa.Publisher's versio

Localization for Yang-Mills Theory on the Fuzzy Sphere

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions from critical points of the action, which are evaluated explicitly. The partition function of ordinary Yang-Mills theory on the sphere is recovered in the classical limit as a sum over instantons. We also apply abelian localization techniques and the geometry of symmetric spaces to derive an explicit combinatorial expression for the partition function, and compare the two approaches. These extend the standard techniques for solving gauge theory on the sphere to the fuzzy case in a rigorous framework.Comment: 55 pages. V2: references added; V3: minor corrections, reference added; Final version to be published in Communications in Mathematical Physic